On the maximum curvature of closed curves in negatively curved manifolds

Simon Brendle, Otis Chodosh

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

Motivated by Almgren's work on the isoperimetric inequality, we prove a sharp inequality relating the length andmaximumcurvature of a closed curve in a complete, simply connectedmanifold of sectional curvature at most -1. Moreover, if equality holds, then the norm of the geodesic curvature is constant and the torsion vanishes. The proof involves an application of the maximum principle to a function deûned on pairs of points.

Original languageEnglish (US)
Pages (from-to)713-722
Number of pages10
JournalCanadian Mathematical Bulletin
Volume58
Issue number4
DOIs
StatePublished - Dec 2015

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • Curvature
  • Manifold

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